00:01
The scenario for this question is a tv reporter says that the proposed constitutional amendment is likely to win approval because for a poll of 847 likely voters, 52%, or a proportion of 0 .52, would vote in favor.
00:21
Furthermore, the reporter says that the margin of error for this poll was 4%.
00:27
And for part a we were asked to explain why the poll is actually inconclusive.
00:33
The reporter should be using some level of a confidence for their estimate.
00:39
So a confidence interval is calculated as the sample proportion plus or minus the margin of error.
00:50
So that's 0 .52 plus or minus 0 .04.
00:55
That's 4%.
00:58
And this gives us a confidence interval ranging from 0 .48 to 0 .5 .6.
01:05
So the problem is with whatever confidence level that the reporter used and the confidence level dictates the margin of error, the estimate or the confidence interval includes values that are below 50%.
01:23
It goes all the way down to 0 .48.
01:26
So that means that proportions less than 50%, as well as above 50%, are compatible with this level of confidence.
01:36
And so the correct answer here is c.
01:40
And that is the poll is inconclusive because 50 % is included in the confidence interval.
01:51
And then for part b we're asked what confidence level the poster is used...